This 'desert island' is a Danish artist's muse

Charles Darwent travels to Laeso to see why it inspires Per Kirkeby, this summer's star of Tate Modern

Until this spring, I knew exactly two things about Laeso: that it was home to a mythological Norse giant called Aegir, and that Per Kirkeby has a studio there.

Neither was entirely enticing. Aegir's wife, Ran, spent her days whipping up hurricanes to sink ships. And when I interviewed Kirkeby in Copenhagen in April – the grand old man of Danish art is the star of Tate Modern this summer – he admitted hating the colour green. "This," he said, gesturing at his immaculate lawn, "is shit." Laeso promised to be stormy and dun-coloured. No one I met, Danes included, seemed to have been there.

Yet, from the ferry, my first sight of Laeso – an island 12 miles long and two miles wide – is green and sunny. It's hot, even. One of Denmark's so- called Desert Isles, it gets little rain from April to September which makes it a summering place of choice for well-heeled Copenhageners. If few other types go to Laeso, it is because the 90-minute ride across the Kattegat from Frederikshavn costs £100 for a car-full to cross, and there is almost nowhere to stay when you get there: a handful of small hotels and guesthouses, mostly in the dinky ports of Vestero and Osterby Havn. Those Copenhageners who don't own the pretty farmhouses tucked up in meadows of wildflowers have to rent them.

One of these, its garden dotted with his trademark brick sculptures, belongs to Per Kirkeby. It seems an odd place for a chlorophobic to have built a studio. Laesoers have been making salt for 900 years, and salt-making had stripped the island of trees by the 1600s. Replanting began after the Second World War, and Laeso is now covered in alder and spruce. Both are green as can be, which must annoy Kirkeby mightily.

Still, from August on, the woods are full of chanterelles which feature on the menus of the island's few, but excellent, restaurants. We stop at one of these, called Spegeriet, run by a cheery man with curled moustaches. The food is fantastic – three kinds of home-cured herring; ham from a farm down the road; and langoustines that were scuttling across the seabed an hour before. Laeso's woods are also home to a rare colony of Apis mellifera mellifera, aka the Northern Brown Bee, and Spegeriet sells jars of home-made honey-and-salt relishes. Some are deeply strange; the cured-walnut combo turns out to be delicious.

One end of Per Kirkeby's house is thatched and, uniquely to Laeso, the thatch is made of seaweed. This has several advantages, among them that the roofs are fireproof and can be repaired simply by slapping more seaweed on them. Because of this, they are often yards thick, sitting on their half-timbered hosts like huge Beatles wigs. Huts are a recurring theme in Kirkeby's painting – the simplest unit of dwelling, as bricks are of building – and you can see why. Laeso's hairy cottages have an elemental feel to them, the kind of place you can imagine a giant and his wife setting up house.

Actually, the farms are more likely to be owned by artists nowadays. Kirkeby hasn't been alone in finding the island a good place to work. Danish Golden Age painters came here, and the Situationist, Asger Jorn – one of Kirkeby's heroes – had a house on Laeso until his death in 1973. (Jorn fell to chatting to a farmer on a train and bought the house without seeing it.)

Near the hamlet of Bangsbo, Jorn's cottage is arranged according to his theory of Triolectics – this included rules for three-sided football. So, each wall has three windows and each window three panes. Nothing has been touched since the day the artist died: dusty bicycles lean against a wall, and a pair of small yellow wellies, once belonging to Jorn's infant son, Ib, sit by the door. Happily, the house was recently sold by Jorn's widow to a Copenhagen gallerist who plans to open it as a retreat for young artists in August.

There's art all over Laeso, much of it unexpected. Top of this category is a jolly lady in Osterby called Anne Julie, who makes art-pipes – burr walnut sculptures that happen to be smokeable. If your pockets are deep enough (an original can set you back £5,000), you can puff away on a can-can dancer's leg or a tulip. If smoke-free art is more your thing, then the medieval wall paintings of Vestero church are unmissable, their Three Kings riding in triple procession around a triptych altar. Jorn would have approved.

The real point of Laeso, though, is that there is nothing much to do there. You can swim, or you can walk along endless miles of empty, sandy beaches looking for amber. You can stand on the deck of your house and watch hares box in the dunes, then peer through a telescope at the distant ferry buffeting its way across from Frederikshavn. You can cycle to the harbour before breakfast and buy fresh lobsters from a fishing boat; you can hitch a ride on a tractor out to the Ronne salt marshes from a farmer who looks like Ernest Hemingway, and listen to curlews and skylarks. You can watch the Kattegat change from turquoise to mercury as the sun goes down. Whatever Per Kirkeby says, green has its advantages.

Compact facts

How to get there

Charles Darwent flew to Aalborg with Norwegian Airlines (020-8099 7254; norwegian.com), which offers return flights from €132. Frederikshavn is a 40-minute drive from Aalborg airport; the ferry makes the 90-minute crossing to Laeso five times a day and costs from DKK200 (£22) per adult return (00 45 98 49 90 22; laesoe-line.dk). To book a house on Laeso go to teamlaesoe.dk. They cost from £300 to £1,000 per week depending on season and size.

Further information

An exhibition of Per Kirkeby's work at London's Tate Modern (tate.org.uk) runs until 6 September. Visit Denmark (visit denmark.com).